Group #19143689 — subgroups

Subgroups — #19143689

Order 5504.

322 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 161 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583456	C₂	1	1	yes	maximal, characteristic
2	#14583029	C₂	1	2	yes	maximal, complemented
3	#14583028	C₂	1	4	yes	maximal, complemented
4	C₈×Dic₈₆	C₂	1	2	yes	maximal, complemented
5	#14582957	C₂	1	4	yes	maximal
6	#14582956	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#431	C₂	1	1	yes	maximal, characteristic
8	#13063325	C₄	1	1	yes	characteristic
9	#13063325	C₄	1	1	yes	characteristic
10	#13063317	C₄	1	2	yes	—
11	#13063304	C₄	1	2	yes	—
12	#13063304	C₄	1	2	yes	—
13	C₄×Dic₈₆	C₂²	1	2	yes	—
14	C₄×Dic₈₆	C₂²	1	2	yes	—
15	#13063284	C₂²	1	2	yes	—
16	C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
17	Dic₄₃⋊C₈	C₂²	1	4	yes	—
18	Dic₄₃⋊C₈	C₂²	1	4	yes	—
19	C₂²⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
20	#13063236	C₂²	1	2	yes	—
21	#13063235	C₂²	1	4	yes	—
22	C₈×Dic₄₃	C₂²	1	4	yes	—
23	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
24	C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
25	C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
26	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
27	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
28	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
31	C₂×Dic₈₆	C₂×C₄	1	2	yes	—
32	C₂×Dic₈₆	C₂×C₄	1	2	yes	—
33	C₂×C₈×C₄₃	C₂³	1	2	yes	—
34	C₂×C₈×C₄₃	C₂³	1	2	yes	—
35	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
36	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
37	C₄²×C₄₃	C₂³	1	1	yes	characteristic
38	C₄²×C₄₃	C₂³	1	1	yes	characteristic
39	C₂²⋊Dic₄₃	C₂×C₄	1	4	yes	—
40	C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
41	C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
42	C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
43	C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
44	Dic₄₃⋊C₄	C₂×C₄	1	4	yes	—
45	Dic₄₃⋊C₄	C₂×C₄	1	4	yes	—
46	C₄×Dic₄₃	C₂³	1	4	yes	—
47	C₂×C₄₃⋊C₈	C₂³	1	4	yes	—
48	C₂³×C₄₃	C₂²×C₄	1	1	yes	characteristic
49	C₂×C₄×C₄₃	—	2	2	no	—
50	C₂×C₄×C₄₃	—	2	2	no	—
51	C₂×C₄×C₄₃	—	4	1	no	—
52	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
53	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
54	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
55	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
56	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
57	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
58	C₂×Dic₄₃	C₂²×C₄	1	4	yes	—
59	C₂×Dic₄₃	C₂²×C₄	1	4	yes	—
60	Dic₈₆	—	2	4	no	—
61	Dic₈₆	—	4	2	no	—
62	C₈×C₄₃	—	2	2	no	—
63	C₈×C₄₃	—	2	2	no	—
64	C₄₃⋊C₈	—	2	4	no	—
65	C₂²×C₄₃	—	2	1	no	—
66	C₂²×C₄₃	—	2	1	no	—
67	C₂²×C₄₃	—	2	1	no	—
68	C₂²×C₄₃	C₂³×C₄	1	1	yes	characteristic
69	C₄×C₄₃	—	2	1	no	—
70	C₄×C₄₃	—	2	1	no	—
71	C₄×C₄₃	—	2	1	no	—
72	C₄×C₄₃	—	2	1	no	—
73	C₄×C₄₃	#131	1	2	yes	—
74	C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
75	Dic₄₃	—	2	4	no	—
76	Dic₄₃	—	2	4	no	—
77	#2985	—	43	1	no	maximal, Sylow
78	C₂×C₄₃	—	4	1	no	—
79	C₂×C₄₃	#519	1	1	yes	characteristic
80	C₂×C₄₃	C₂×#131	1	1	yes	characteristic
81	C₂×C₄₃	#568	1	1	yes	characteristic
82	#533	—	43	1	no	—
83	#446	—	43	4	no	—
84	#446	—	43	2	no	—
85	C₈×Q₈	—	43	2	no	—
86	#433	—	43	4	no	—
87	#432	—	43	1	no	—
88	#431	D₄₃	1	1	yes	characteristic
89	C₄₃	#2985	1	1	yes	characteristic, complemented, Sylow
90	C₄⋊Q₈	—	43	1	no	—
91	C₄⋊Q₈	—	43	1	no	—
92	#125	—	43	2	no	—
93	C₂²⋊Q₈	—	43	2	no	—
94	C₂²⋊Q₈	—	43	2	no	—
95	C₄×Q₈	—	43	2	no	—
96	C₄×Q₈	—	43	2	no	—
97	#117	—	43	2	no	—
98	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
99	C₄⋊C₈	—	43	4	no	—
100	C₄⋊C₈	—	43	4	no	—
101	C₄⋊C₈	—	43	2	no	—
102	C₄⋊C₈	C₂×D₄₃	1	2	yes	—
103	C₂²⋊C₈	—	43	2	no	—
104	C₂²⋊C₈	C₂×D₄₃	1	2	yes	—
105	#97	—	43	4	no	—
106	#97	—	43	2	no	—
107	C₄×C₈	—	43	4	no	—
108	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
109	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
110	C₂×Q₈	—	43	2	no	—
111	C₂×Q₈	—	43	2	no	—
112	C₂²×C₄	C₄×D₄₃	1	1	yes	characteristic
113	C₂²×C₄	C₄×D₄₃	1	1	yes	characteristic
114	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
115	C₂×C₈	—	43	4	no	—
116	C₂×C₈	C₂²×D₄₃	1	2	yes	—
117	C₂×C₈	C₂²×D₄₃	1	2	yes	—
118	C₄⋊C₄	—	43	2	no	—
119	C₄⋊C₄	—	43	2	no	—
120	C₄⋊C₄	—	43	4	no	—
121	C₄⋊C₄	—	43	4	no	—
122	C₄⋊C₄	—	43	2	no	—
123	C₄⋊C₄	—	43	2	no	—
124	C₂²⋊C₄	—	43	4	no	—
125	C₄²	—	43	4	no	—
126	C₄²	C₄×D₄₃	1	1	yes	characteristic
127	C₄²	C₄×D₄₃	1	1	yes	characteristic
128	C₄²	C₂²×D₄₃	1	1	yes	characteristic
129	C₄²	C₂²×D₄₃	1	1	yes	characteristic
130	C₂³	C₂×C₄×D₄₃	1	1	yes	characteristic
131	Q₈	—	86	4	no	—
132	Q₈	—	172	2	no	—
133	C₂×C₄	—	2	2	no	—
134	C₂×C₄	—	2	2	no	—
135	C₂×C₄	—	4	1	no	—
136	C₂×C₄	—	43	4	no	—
137	C₂×C₄	—	43	4	no	—
138	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
139	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
140	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
141	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
142	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
143	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
144	C₈	—	2	2	no	—
145	C₈	—	2	2	no	—
146	C₈	—	86	4	no	—
147	C₂²	—	2	1	no	—
148	C₂²	—	2	1	no	—
149	C₂²	—	2	1	no	—
150	C₂²	C₂²×C₄×D₄₃	1	1	yes	characteristic
151	C₄	—	2	1	no	—
152	C₄	—	2	1	no	—
153	C₄	—	2	1	no	—
154	C₄	—	2	1	no	—
155	C₄	—	86	4	no	—
156	C₄	—	86	4	no	—
157	C₄	#13063331	1	2	yes	—
158	C₄	#13063372	1	2	yes	—
159	C₂	—	4	1	no	—
160	C₂	#14583376	1	1	yes	characteristic
161	C₂	C₂×#13063331	1	1	yes	characteristic
162	C₂	#14583665	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583456

C₂

yes

maximal, characteristic

#14583029

C₂

yes

maximal, complemented

#14583028

C₂

yes

maximal, complemented

C₈×Dic₈₆

C₂

yes

maximal, complemented

#14582957

C₂

yes

maximal

#14582956

C₂

yes

maximal, characteristic

C₄₃×#431

C₂

yes

maximal, characteristic

#13063325

C₄

yes

characteristic

#13063325

C₄

yes

characteristic

#13063317

C₄

yes

—

#13063304

C₄

yes

—

#13063304

C₄

yes

—

C₄×Dic₈₆

C₂²

yes

—

C₄×Dic₈₆

C₂²

yes

—

#13063284

C₂²

yes

—

C₄⋊(C₄₃⋊C₈)

C₂²

yes

—

Dic₄₃⋊C₈

C₂²

yes

—

Dic₄₃⋊C₈

C₂²

yes

—

C₂²⋊(C₄₃⋊C₈)

C₂²

yes

—

#13063236

C₂²

yes

—

#13063235

C₂²

yes

—

C₈×Dic₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₄⋊C₈×C₄₃

C₂²

yes

—

C₂²⋊C₈×C₄₃

C₂²

yes

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂×Dic₈₆

C₂×C₄

yes

—

C₂×Dic₈₆

C₂×C₄

yes

—

C₂×C₈×C₄₃

C₂³

yes

—

C₂×C₈×C₄₃

C₂³

yes

—

C₄²×C₄₃

C₂×C₄

yes

characteristic

C₄²×C₄₃

C₂×C₄

yes

characteristic

C₄²×C₄₃

C₂³

yes

characteristic

C₄²×C₄₃

C₂³

yes

characteristic

C₂²⋊Dic₄₃

C₂×C₄

yes

—

C₄⋊Dic₄₃

C₂×C₄

yes

—

C₄⋊Dic₄₃

C₂×C₄

yes

—

C₄⋊Dic₄₃

C₂×C₄

yes

—

C₄⋊Dic₄₃

C₂×C₄

yes

—

Dic₄₃⋊C₄

C₂×C₄

yes

—

Dic₄₃⋊C₄

C₂×C₄

yes

—

C₄×Dic₄₃

C₂³

yes

—

C₂×C₄₃⋊C₈

C₂³

yes

—

C₂³×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂⁴

yes

characteristic

C₂×Dic₄₃

C₂²×C₄

yes

—

C₂×Dic₄₃

C₂²×C₄

yes

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂³×C₄

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#131

yes

—

C₄×C₄₃

2₋¹⁺⁴

yes

—

Dic₄₃

—

Dic₄₃

—

#2985

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

—

—

C₈×Q₈

—

#433

—

#432

—

#431

D₄₃

yes

characteristic

C₄₃

#2985

yes

characteristic, complemented, Sylow

C₄⋊Q₈

—

C₄⋊Q₈

—

#125

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

C₄×Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

C₄⋊C₈

—

100

C₄⋊C₈

—

101

C₄⋊C₈

—

102

C₄⋊C₈

C₂×D₄₃

yes

—

103

C₂²⋊C₈

—

104

C₂²⋊C₈

C₂×D₄₃

yes

—

105

#97

—

106

#97

—

107

C₄×C₈

—

108

C₄×C₈

C₂×D₄₃

yes

characteristic

109

C₄×C₈

C₂×D₄₃

yes

characteristic

110

C₂×Q₈

—

111

C₂×Q₈

—

112

C₂²×C₄

C₄×D₄₃

yes

characteristic

113

C₂²×C₄

C₄×D₄₃

yes

characteristic

114

C₂²×C₄

C₂²×D₄₃

yes

characteristic

115

C₂×C₈

—

116

C₂×C₈

C₂²×D₄₃

yes

—

117

C₂×C₈

C₂²×D₄₃

yes

—

118

C₄⋊C₄

—

119

C₄⋊C₄

—

120

C₄⋊C₄

—

121

C₄⋊C₄

—

122

C₄⋊C₄

—

123

C₄⋊C₄

—

124

C₂²⋊C₄

—

125

C₄²

—

126

C₄²

C₄×D₄₃

yes

characteristic

127

C₄²

C₄×D₄₃

yes

characteristic

128

C₄²

C₂²×D₄₃

yes

characteristic

129

C₄²

C₂²×D₄₃

yes

characteristic

130

C₂³

C₂×C₄×D₄₃

yes

characteristic

131

Q₈

—

132

Q₈

—

172

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

139

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

140

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

141

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

142

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

143

C₂×C₄

C₂³×D₄₃

yes

characteristic

144

C₈

—

145

C₈

—

146

C₈

—

147

C₂²

—

148

C₂²

—

149

C₂²

—

150

C₂²

C₂²×C₄×D₄₃

yes

characteristic

151

C₄

—

152

C₄

—

153

C₄

—

154

C₄

—

155

C₄

—

156

C₄

—

157

C₄

#13063331

yes

—

158

C₄

#13063372

yes

—

159

C₂

—

160

C₂

#14583376

yes

characteristic

161

C₂

C₂×#13063331

yes

characteristic

162

C₂

#14583665

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₄₃
commutator, socle	C₂²×C₄₃	C₂³×C₄
Fitting	C₄₃×#431	C₂
hypercenter	#431	D₄₃
hypocenter	C₄₃	#2985
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ #431

subgroup

G/H

center, Frattini

C₂×C₄

C₂³×D₄₃

commutator, socle

C₂²×C₄₃

C₂³×C₄

Fitting

C₄₃×#431

C₂

D₄₃

C₄₃

G ▷ C₂²×C₄₃ ▷ C₄₃

C₁ ◁ C₂×C₄ ◁ #431

N	H ≅ G/N	type
2. #14583029	C₂	semidirect
3. #14583028	C₂	semidirect
4. C₈×Dic₈₆	C₂	semidirect
89. C₄₃	#2985	semidirect

H ≅ G/N

type

2. #14583029

C₂

semidirect

3. #14583028

C₂

semidirect

4. C₈×Dic₈₆

C₂

semidirect

89. C₄₃

#2985

semidirect

Subgroups — #19143689

Conjugacy classes of subgroups

Complements